How do you type fractional lengths into blender?
I suppose you are talking about the numerical input of Modal Operators, because in ordinary input field you can input a python expression with no problems.

In modal operators it is different. Numerical input works fine, but the divide / and minus - keys function as toggles instead. / toggles between {input} and 1/{input}.

There is however an expression mode you can enter by pressing the = key first (* also works, which is close on numpad). You can now enter any expression, like 3/2 or 3-2 and it works.

I like to do this rather than having to apply the operator in 2 steps: 1st for the numerator and 2nd for the 1/denominator to have a resulting numerator/denominator transformation.

Note: correct order matters. If you press  / first, you enter into 1/{..} mode. Then if you enter expression mode, you cannot go back and get rid of the 1/{..}. You have to cancel the operator.